1. On the constrained error bound condition and the projected Levenberg–Marquardt method.
- Author
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Behling, R., Fischer, A., Haeser, G., Ramos, A., and Schönefeld, K.
- Subjects
- *
ERROR analysis in mathematics , *INTERSECTION theory , *MATHEMATICAL bounds , *MANIFOLDS (Mathematics) , *MARQUARDT algorithm , *SET theory - Abstract
In this paper, we first derive a characterization of the solution set of a continuously differentiable system of equations subject to a closed feasible set. Assuming that a constrained local error bound condition is satisfied, we prove that the solution set can locally be written as the intersection of a differentiable manifold with the feasible set. Based on the derivation of this result, we then show that the projected Levenberg–Marquardt method converges locally R-linearly to a possibly nonisolated solution under significantly weaker conditions than previously done. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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